Section 4.3.6.2. Relations between symmetry elements

Conventionally, the representative directions of the primary, secondary and tertiary symmetry elements are chosen as [001], [111], and [] (cf. Table 2.2.4.1 for the equivalent directions). As in tetragonal and hexagonal space groups, tertiary symmetry elements are not independent. In classes 432, and , there are product rules where the tertiary symmetry element is in parentheses; analogous rules hold for the space groups belonging to these classes. When the symmetry directions of the primary and secondary symmetry elements are chosen along [001] and [111], respectively, the tertiary symmetry direction is [011], according to the product rule. In order to have the tertiary symmetry direction along [], one has to choose the somewhat awkward primary and secondary symmetry directions [010] and [].